This invention relates to a deburring tool and more particularly a tool for machining the opening rims of bores which embodies a shaft and a cutter that radially protrudes from the shaft. In the deburring tool art it is known to provide a cutter body having a rockable cutter therein which is spring urged outwardly so as to protrude from a slot in the tool body. Such a type of tool is shown in U.S. Pat. No. 2,895,356. Another form of deburring tool that is known in the art and one which has diametrically opposed cutters is shown, for example, in U.S. Pat. No. 3,661,473. In this type of tool the tool part is longitudinally slit so that the cutting portions which are generally made part of the outer end of the tool may have some outward resiliency due to the spring action of the resulting fork-like end. It has been found that there are some difficulties with the first type of device particularly since it is relatively complicated and difficult to manufacture and further the recess in the shaft which receives the cutter and the pivoting shaft or axle upon which the cutter must rotate become difficult to manufacture and replacement of a worn cutter is complicated. In the second form of known deburring type tools the tool is suitable only for relatively small bore diameters since the resilient parts of the shaft formed by the fork or longitudinal slot structure tend to set up vibrations, and if strengthening is provided, then the two portions are not adequately resilient. Further since the cutting blades are integral with the head end of the tool and the fork limbs, there is no interchangeability of cutting edges and the tool body must effectively be re-ground when there is difficulty experienced. The instant invention provides a simpler tool which obviates the aforementioned difficulties and which is particularly suitable for large bore diameters.